Approximate String Matching by Finite Automata

Abs t r ac t . Approximate string matching is a sequential problem and therefore it is possible to solve it using finite automata. A nondeterministic finite automaton is constructed for string matching with k mismatches. It is shown, how "dynamic programming" and "shift-and" based algorithms simulate this nondeterministic finite automaton. The corresponding deterministic finite automaton have O(m TM) states, where m is the length of the pattern and k is the number of mismatches. The time complexity of algorithms based on such deterministic finite automaton is O(n), where n is the length of text.